Summary: Tight Bounds for Shared Memory Systems Accessed
by Byzantine Processes
Noga Alon
Michael Merritt
Omer Reingold§
Gadi Taubenfeld¶
Rebecca N. Wright
June 15, 2005
Abstract
We provide efficient constructions and tight bounds for shared memory systems accessed by n pro-
cesses, up to t of which may exhibit Byzantine failures, in a model previously explored by Malkhi et
al. [MMRT03]. We show that sticky bits are universal in the Byzantine failure model for n 3t + 1, an
improvement over the previous result requiring n (2t + 1)(t + 1). Our result follows from a new strong
consensus construction that uses sticky bits and tolerates t Byzantine failures among n processes for any
n 3t + 1, the best possible bound on n for strong consensus. We also present tight bounds on the
efficiency of implementations of strong consensus objects from sticky bits and similar primitive objects.
1 Introduction
Although Byzantine fault tolerance in message-passing systems has been extensively investigated, it was only
recently that Malkhi et al. initiated the study of Byzantine fault tolerance in asynchronous shared memory
systems [MMRT03]. Their work establishes a formal model and shows how the use of access control lists